Research on High Power Factor Single Tube Variable Structure Wireless Power Transmission

Aiming at the problems existing in the current radio energy transmission system, we propose a wireless power transmission (WPT) system with the parallel–parallel (PP)-compensated structure. The transmitter of the transmission system adopts a separate topological structure to suppress the current shock and noise. In order to improve the efficiency of the WPT, reduce the static loss, and reduce the current oscillation loss on the power side, the input current ripple can be improved by two parallel phase-shifting methods. In this paper, two topological theories are analyzed, and the simulation and experiment results verify the correctness of these theories under both static and on-load conditions. After the final two-way phase-shift, 61.99% of the ripple is reduced. It provides a new approach for the design of WPT systems with PP structure.

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs

We propose a novel procedure of assigning a pair of non-unitary topological quantum field theories (TQFTs), TFT±[$$ \mathcal{T} $$ T rank 0], to a (2+1)D interacting $$ \mathcal{N} $$ N = 4 superconformal field theory (SCFT) $$ \mathcal{T} $$ T rank 0 of rank 0, i.e. having no Coulomb and Higgs branches. The topological theories arise from particular degenerate limits of the SCFT. Modular data of the non-unitary TQFTs are extracted from the supersymmetric partition functions in the degenerate limits. As a non-trivial dictionary, we propose that F = maxα (− log|$$ {S}_{0\alpha}^{\left(+\right)} $$ S 0 α + |) = maxα (− log|$$ {S}_{0\alpha}^{\left(-\right)} $$ S 0 α − |), where F is the round three-sphere free energy of $$ \mathcal{T} $$ T rank 0 and $$ {S}_{0\alpha}^{\left(\pm \right)} $$ S 0 α ± is the first column in the modular S-matrix of TFT±. From the dictionary, we derive the lower bound on F, F ≥ − log $$ \left(\sqrt{\frac{5-\sqrt{5}}{10}}\right) $$ 5 − 5 10 ≃ 0.642965, which holds for any rank 0 SCFT. The bound is saturated by the minimal $$ \mathcal{N} $$ N = 4 SCFT proposed by Gang-Yamazaki, whose associated topological theories are both the Lee-Yang TQFT. We explicitly work out the (rank 0 SCFT)/(non-unitary TQFTs) correspondence for infinitely many examples.

Embedding Gauss–Bonnet Scalarization Models in Higher Dimensional Topological Theories

In the presence of appropriate non-minimal couplings between a scalar field and the curvature squared Gauss–Bonnet (GB) term, compact objects such as neutron stars and black holes (BHs) can spontaneously scalarize, becoming a preferred vacuum. Such strong gravity phase transitions have attracted considerable attention recently. The non-minimal coupling functions that allow this mechanism are, however, always postulated ad hoc. Here, we point out that families of such functions naturally emerge in the context of Higgs–Chern–Simons gravity models, which are found as dimensionally descents of higher dimensional, purely topological, Chern–Pontryagin non-Abelian densities. As a proof of concept, we study spherically symmetric scalarized BH solutions in a particular Einstein-GB-scalar field model, whose coupling is obtained from this construction, pointing out novel features and caveats thereof. The possibility of vectorization is also discussed, since this construction also originates vector fields non-minimally coupled to the GB invariant.

Dynamical generalization of Yetter’s model based on a crossed module of discrete groups

We construct a lattice model based on a crossed module of possibly non-abelian finite groups. It generalizes known topological quantum field theories, but in contrast to these models admits local physical excitations. Its degrees of freedom are defined on links and plaquettes, while gauge transformations are based on vertices and links of the underlying lattice. We specify the Hilbert space, define basic observables (including the Hamiltonian) and initiate a discussion on the model’s phase diagram. The constructed model reduces in appropriate limits to topological theories with symmetries described by groups and crossed modules, lattice Yang-Mills theory and 2-form electrodynamics. We conclude by reviewing classifying spaces of crossed modules, with an emphasis on the direct relation between their geometry and properties of gauge theories under consideration.

Area-Dependent Quantum Field Theory

Area-dependent quantum field theory is a modification of two-dimensional topological quantum field theory, where one equips each connected component of a bordism with a positive real number—interpreted as area—which behaves additively under glueing. As opposed to topological theories, in area-dependent theories the state spaces can be infinite-dimensional. We introduce the notion of regularised Frobenius algebras in Hilbert spaces and show that area-dependent theories are in one-to-one correspondence to commutative regularised Frobenius algebras. We also provide a state sum construction for area-dependent theories. Our main example is two-dimensional Yang–Mills theory with compact gauge group, which we treat in detail.

From QFT to 2-d Supersymetric TQT:Mirror symmetry between Math and Physic

Theoretical physics is taking an increasing part in the universe of mathematics. After calculus, vector and tensorial analysis, topological theories make their entry into quantum field theories. More precisely, in this domain, topological theories are the most relevant. A fundamental theorem of the Atiyah has important repercussions in several branches of quantum physics in the geometric approach. We can cite the work of Alain Connes on non-commutative geometry, but also all the developments due to Donaldson, E. Witten around Gauge theories, superstring and Mirror Symmetry. We present here an historical survey of some topological field theories, especially Mirror Symmetry to understand the interpenetration between quantum physics and topology.

Topological Gravity Motivated by Renormalization Group

Recently, we have proposed models of topological field theory including gravity in Mod. Phys. Lett. A 2016, 31, 1650213 and Phys. Rev. D 2017, 96, 024009, in order to solve the problem of the cosmological constant. The Lagrangian densities of the models are BRS (Becchi-Rouet-Stora) exact and therefore the models can be regarded as topological theories. In the models, the coupling constants, including the cosmological constant, look as if they run with the scale of the universe and its behavior is very similar to the renormalization group. Motivated by these models, we propose new models with an the infrared fixed point, which may correspond to the late time universe, and an ultraviolet fixed point, which may correspond to the early universe. In particular, we construct a model with the solutions corresponding to the de Sitter space-time both in the ultraviolet and the infrared fixed points.